Mathematics is an extraordinary exercise of the human mind in abstracting the results of observation to find similarities and differences between phenomena. These relations between phenomena make it possible to organize the natural world into discrete sets of objects that can be studied using similar mathematical objects and methods.
Nature, as an object of mathematical study, bridges the gap between the concreteness of the everyday environment and the abstraction of mathematics. Mathematics, in turn, allows us to summarize, formalize, interpolate, and extrapolate from observations that have been recorded.
